Numerical simulation of the water-ice phase transition in highly permeable water-saturated porous media

Abstract

Modeling a phase transition in porous media is a complex mathematical problem that is often encountered in practice. For its successful solution, it is necessary to take into account many parameters, in particular, the convective movement of unfrozen water. Free convective currents in a porous medium, of course, affect the process of phase transition during its freezing, but it is obvious that in some cases the influence of this phenomenon can be neglected. The purpose of this work is to study the mechanisms and degree of influence of free convection on the freezing of a water-saturated porous medium. The phase transition in a porous medium was simulated numerically, taking into account the inversion of the water density. The role of the convective flow on the crystallization of water in a porous medium was studied, as well as the influence of the selected water model on convective flows in order to obtain criteria that determine the need to take into account these physical phenomena and properties in solving thermophysical problems with a phase transition in porous media, which can significantly simplify the modeled system. An axisymmetric model problem with a vertical cooling element immersed in a water-saturated porous medium is solved. The temperature of the cooling element changed slowly, and the temperature at the outer boundary of the porous medium was maintained constant. The influence of convective heat transfer on the process of phase transition in a porous medium is estimated taking into account the phenomenon of water density inversion. It is shown that the presence of a water density maximum significantly determines the process of phase transition in porous media. In comparison with numerical models that do not take into account the phenomenon of density inversion, when using the real water model, the flow is restructured, the intensity of the convective flow decreases, and the volume of ice formed increases. The influence of the permeability of a porous medium on the structure of the resulting convective flow has been studied; with a decrease in permeability, the presence of a density maximum leads to a decrease in the role of convective heat transfer, which in most cases makes it possible to ignore it in problems with an ice-water phase transition in porous media.